Conformal Riemannian And Lagrangian Geometry

Author : Sun-Yung A. Chang
Publisher : American Mathematical Soc.
Page : 97 pages
File Size : 51,6 Mb
Release : 2002
Category : Mathematics
ISBN : 9780821832103

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Conformal, Riemannian and Lagrangian Geometry by Sun-Yung A. Chang Pdf

Recent developments in topology and analysis have led to the creation of new lines of investigation in differential geometry. The 2000 Barrett Lectures present the background, context and main techniques of three such lines by means of surveys by leading researchers. The first chapter (by Alice Chang and Paul Yang) introduces new classes of conformal geometric invariants, and then applies powerful techniques in nonlinear differential equations to derive results on compactificationsof manifolds and on Yamabe-type variational problems for these invariants. This is followed by Karsten Grove's lectures, which focus on the use of isometric group actions and metric geometry techniques to understand new examples and classification results in Riemannian geometry, especially inconnection with positive curvature. The chapter written by Jon Wolfson introduces the emerging field of Lagrangian variational problems, which blends in novel ways the structures of symplectic geometry and the techniques of the modern calculus of variations. The lectures provide an up-do-date overview and an introduction to the research literature in each of their areas. The book is a very enjoyable read, which should prove useful to graduate students and researchers in differential geometryand geometric analysis.

Author : Sun-Yung A. Chang
Publisher : American Mathematical Soc.
Page : 85 pages
File Size : 48,5 Mb
Release : 2002
Category : Mathematics
ISBN : 1470421739

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Conformal, Riemannian and Lagrangian Geometry by Sun-Yung A. Chang Pdf

Developments in topology and analysis have led to the creation of new lines of investigation in differential geometry. The 2000 Barrett Lectures present the background, context and main techniques of three such lines by means of surveys by researchers.

Author : Maks A. Akivis,Vladislav V. Goldberg
Publisher : John Wiley & Sons
Page : 404 pages
File Size : 49,8 Mb
Release : 2011-09-20
Category : Mathematics
ISBN : 9781118030882

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Conformal Differential Geometry and Its Generalizations by Maks A. Akivis,Vladislav V. Goldberg Pdf

Comprehensive coverage of the foundations, applications, recent developments, and future of conformal differential geometry Conformal Differential Geometry and Its Generalizations is the first and only text that systematically presents the foundations and manifestations of conformal differential geometry. It offers the first unified presentation of the subject, which was established more than a century ago. The text is divided into seven chapters, each containing figures, formulas, and historical and bibliographical notes, while numerous examples elucidate the necessary theory. Clear, focused, and expertly synthesized, Conformal Differential Geometry and Its Generalizations * Develops the theory of hypersurfaces and submanifolds of any dimension of conformal and pseudoconformal spaces. * Investigates conformal and pseudoconformal structures on a manifold of arbitrary dimension, derives their structure equations, and explores their tensor of conformal curvature. * Analyzes the real theory of four-dimensional conformal structures of all possible signatures. * Considers the analytic and differential geometry of Grassmann and almost Grassmann structures. * Draws connections between almost Grassmann structures and web theory. Conformal differential geometry, a part of classical differential geometry, was founded at the turn of the century and gave rise to the study of conformal and almost Grassmann structures in later years. Until now, no book has offered a systematic presentation of the multidimensional conformal differential geometry and the conformal and almost Grassmann structures. After years of intense research at their respective universities and at the Soviet School of Differential Geometry, Maks A. Akivis and Vladislav V. Goldberg have written this well-conceived, expertly executed volume to fill a void in the literature. Dr. Akivis and Dr. Goldberg supply a deep foundation, applications, numerous examples, and recent developments in the field. Many of the findings that fill these pages are published here for the first time, and previously published results are reexamined in a unified context. The geometry and theory of conformal and pseudoconformal spaces of arbitrary dimension, as well as the theory of Grassmann and almost Grassmann structures, are discussed and analyzed in detail. The topics covered not only advance the subject itself, but pose important questions for future investigations. This exhaustive, groundbreaking text combines the classical results and recent developments and findings. This volume is intended for graduate students and researchers of differential geometry. It can be especially useful to those students and researchers who are interested in conformal and Grassmann differential geometry and their applications to theoretical physics.

Author : Helga Baum,Andreas Juhl
Publisher : Springer Science & Business Media
Page : 161 pages
File Size : 44,6 Mb
Release : 2011-01-28
Category : Mathematics
ISBN : 9783764399092

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Conformal Differential Geometry by Helga Baum,Andreas Juhl Pdf

Conformal invariants (conformally invariant tensors, conformally covariant differential operators, conformal holonomy groups etc.) are of central significance in differential geometry and physics. Well-known examples of such operators are the Yamabe-, the Paneitz-, the Dirac- and the twistor operator. The aim of the seminar was to present the basic ideas and some of the recent developments around Q-curvature and conformal holonomy. The part on Q-curvature discusses its origin, its relevance in geometry, spectral theory and physics. Here the influence of ideas which have their origin in the AdS/CFT-correspondence becomes visible. The part on conformal holonomy describes recent classification results, its relation to Einstein metrics and to conformal Killing spinors, and related special geometries.

Author : Ovidiu Calin,Der-Chen Chang
Publisher : Springer Science & Business Media
Page : 278 pages
File Size : 41,7 Mb
Release : 2006-03-30
Category : Mathematics
ISBN : 9780817644215

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Geometric Mechanics on Riemannian Manifolds by Ovidiu Calin,Der-Chen Chang Pdf

* A geometric approach to problems in physics, many of which cannot be solved by any other methods * Text is enriched with good examples and exercises at the end of every chapter * Fine for a course or seminar directed at grad and adv. undergrad students interested in elliptic and hyperbolic differential equations, differential geometry, calculus of variations, quantum mechanics, and physics

Author : Nail H. Ibragimov
Publisher : Walter de Gruyter GmbH & Co KG
Page : 197 pages
File Size : 55,8 Mb
Release : 2015-08-31
Category : Mathematics
ISBN : 9783110379501

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Tensors and Riemannian Geometry by Nail H. Ibragimov Pdf

This book is based on the experience of teaching the subject by the author in Russia, France, South Africa and Sweden. The author provides students and teachers with an easy to follow textbook spanning a variety of topics on tensors, Riemannian geometry and geometric approach to partial differential equations. Application of approximate transformation groups to the equations of general relativity in the de Sitter space simplifies the subject significantly.

Author : John M. Mackay,Jeremy T. Tyson
Publisher : American Mathematical Soc.
Page : 162 pages
File Size : 45,7 Mb
Release : 2010
Category : Mathematics
ISBN : 9780821852293

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Conformal Dimension by John M. Mackay,Jeremy T. Tyson Pdf

Conformal dimension measures the extent to which the Hausdorff dimension of a metric space can be lowered by quasisymmetric deformations. Introduced by Pansu in 1989, this concept has proved extremely fruitful in a diverse range of areas, including geometric function theory, conformal dynamics, and geometric group theory. This survey leads the reader from the definitions and basic theory through to active research applications in geometric function theory, Gromov hyperbolic geometry, and the dynamics of rational maps, amongst other areas. It reviews the theory of dimension in metric spaces and of deformations of metric spaces. It summarizes the basic tools for estimating conformal dimension and illustrates their application to concrete problems of independent interest. Numerous examples and proofs are provided. Working from basic definitions through to current research areas, this book can be used as a guide for graduate students interested in this field, or as a helpful survey for experts. Background needed for a potential reader of the book consists of a working knowledge of real and complex analysis on the level of first- and second-year graduate courses.

Author : Xianfeng David Gu,Shing-Tung Yau
Publisher : Unknown
Page : 324 pages
File Size : 41,5 Mb
Release : 2008
Category : CD-ROMs
ISBN : UOM:39015080827697

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Computational Conformal Geometry by Xianfeng David Gu,Shing-Tung Yau Pdf

Author : Ana Hurtado,Steen Markvorsen,Maung Min-Oo,Vicente Palmer
Publisher : Springer Nature
Page : 121 pages
File Size : 40,7 Mb
Release : 2020-08-19
Category : Mathematics
ISBN : 9783030552930

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Global Riemannian Geometry: Curvature and Topology by Ana Hurtado,Steen Markvorsen,Maung Min-Oo,Vicente Palmer Pdf

This book contains a clear exposition of two contemporary topics in modern differential geometry: distance geometric analysis on manifolds, in particular, comparison theory for distance functions in spaces which have well defined bounds on their curvature the application of the Lichnerowicz formula for Dirac operators to the study of Gromov's invariants to measure the K-theoretic size of a Riemannian manifold. It is intended for both graduate students and researchers.

Author : Ramesh Sharma,Sharief Deshmukh
Publisher : Springer Nature
Page : 165 pages
File Size : 51,8 Mb
Release : 2024-01-19
Category : Mathematics
ISBN : 9789819992584

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Conformal Vector Fields, Ricci Solitons and Related Topics by Ramesh Sharma,Sharief Deshmukh Pdf

This book provides an up-to-date introduction to the theory of manifolds, submanifolds, semi-Riemannian geometry and warped product geometry, and their applications in geometry and physics. It then explores the properties of conformal vector fields and conformal transformations, including their fixed points, essentiality and the Lichnerowicz conjecture. Later chapters focus on the study of conformal vector fields on special Riemannian and Lorentzian manifolds, with a special emphasis on general relativistic spacetimes and the evolution of conformal vector fields in terms of initial data. The book also delves into the realm of Ricci flow and Ricci solitons, starting with motivations and basic results and moving on to more advanced topics within the framework of Riemannian geometry. The main emphasis of the book is on the interplay between conformal vector fields and Ricci solitons, and their applications in contact geometry. The book highlights the fact that Nil-solitons and Sol-solitons naturally arise in the study of Ricci solitons in contact geometry. Finally, the book gives a comprehensive overview of generalized quasi-Einstein structures and Yamabe solitons and their roles in contact geometry. It would serve as a valuable resource for graduate students and researchers in mathematics and physics as well as those interested in the intersection of geometry and physics.

Author : Gabriel-Eduard Vîlcu
Publisher : MDPI
Page : 208 pages
File Size : 51,6 Mb
Release : 2021-03-09
Category : Mathematics
ISBN : 9783036502984

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Inequalities in Geometry and Applications by Gabriel-Eduard Vîlcu Pdf

This book presents the recent developments in the field of geometric inequalities and their applications. The volume covers a vast range of topics, such as complex geometry, contact geometry, statistical manifolds, Riemannian submanifolds, optimization theory, topology of manifolds, log-concave functions, Obata differential equation, Chen invariants, Einstein spaces, warped products, solitons, isoperimetric problem, Erdös–Mordell inequality, Barrow’s inequality, Simpson inequality, Chen inequalities, and q-integral inequalities. By exposing new concepts, techniques and ideas, this book will certainly stimulate further research in the field.

Author : Fernando Galaz-García,Cecilia González-Tokman,Juan Carlos Pardo Millán
Publisher : American Mathematical Society
Page : 319 pages
File Size : 51,9 Mb
Release : 2021-11-22
Category : Mathematics
ISBN : 9781470465360

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Mexican Mathematicians in the World by Fernando Galaz-García,Cecilia González-Tokman,Juan Carlos Pardo Millán Pdf

Articles in this volume are based on presentations given at the IV Meeting of Mexican Mathematicians Abroad (IV Reunión de Matemáticos Mexicanos en el Mundo), held from June 10–15, 2018, at Casa Matemática Oaxaca (CMO), Mexico. This meeting was the fourth in a series of ongoing biannual meetings bringing together Mexican mathematicians working abroad with their peers in Mexico. This book features surveys and research articles from five broad research areas: algebra, analysis, combinatorics, geometry, and topology. Their topics range from general relativity and mathematical physics to interactions between logic and ergodic theory. Several articles provide a panoramic view of the fields and problems on which the authors are currently working on, showcasing diverse research lines complementary to those currently pursued in Mexico. The research-oriented manuscripts provide either alternative approaches to well-known problems or new advances in active research fields.

Author : Frank Sottile
Publisher : American Mathematical Soc.
Page : 214 pages
File Size : 45,9 Mb
Release : 2011-08-31
Category : Mathematics
ISBN : 9780821853313

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Real Solutions to Equations from Geometry by Frank Sottile Pdf

Understanding, finding, or even deciding on the existence of real solutions to a system of equations is a difficult problem with many applications outside of mathematics. While it is hopeless to expect much in general, we know a surprising amount about these questions for systems which possess additional structure often coming from geometry. This book focuses on equations from toric varieties and Grassmannians. Not only is much known about these, but such equations are common in applications. There are three main themes: upper bounds on the number of real solutions, lower bounds on the number of real solutions, and geometric problems that can have all solutions be real. The book begins with an overview, giving background on real solutions to univariate polynomials and the geometry of sparse polynomial systems. The first half of the book concludes with fewnomial upper bounds and with lower bounds to sparse polynomial systems. The second half of the book begins by sampling some geometric problems for which all solutions can be real, before devoting the last five chapters to the Shapiro Conjecture, in which the relevant polynomial systems have only real solutions.

Author : Antonio Alarcón,Vicente Palmer,César Rosales
Publisher : Springer Nature
Page : 398 pages
File Size : 50,7 Mb
Release : 2023-11-25
Category : Mathematics
ISBN : 9783031399169

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New Trends in Geometric Analysis by Antonio Alarcón,Vicente Palmer,César Rosales Pdf

The aim of this book is to provide an overview of some of the progress made by the Spanish Network of Geometric Analysis (REAG, by its Spanish acronym) since its born in 2007. REAG was created with the objective of enabling the interchange of ideas and the knowledge transfer between several Spanish groups having Geometric Analysis as a common research line. This includes nine groups at Universidad Autónoma de Barcelona, Universidad Autónoma de Madrid, Universidad de Granada, Universidad Jaume I de Castellón, Universidad de Murcia, Universidad de Santiago de Compostela and Universidad de Valencia. The success of REAG has been substantiated with regular meetings and the publication of research papers obtained in collaboration between the members of different nodes. On the occasion of the 15th anniversary of REAG this book aims to collect some old and new contributions of this network to Geometric Analysis. The book consists of thirteen independent chapters, all of them authored by current members of REAG. The topics under study cover geometric flows, constant mean curvature surfaces in Riemannian and sub-Riemannian spaces, integral geometry, potential theory and Riemannian geometry, among others. Some of these chapters have been written in collaboration between members of different nodes of the network, and show the fruitfulness of the common research atmosphere provided by REAG. The rest of the chapters survey a research line or present recent progresses within a group of those forming REAG. Surveying several research lines and offering new directions in the field, the volume is addressed to researchers (including postdocs and PhD students) in Geometric Analysis in the large.

Author : Christian Bär,Joachim Lohkamp,Matthias Schwarz
Publisher : Springer Science & Business Media
Page : 520 pages
File Size : 52,9 Mb
Release : 2011-12-18
Category : Mathematics
ISBN : 9783642228421

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Global Differential Geometry by Christian Bär,Joachim Lohkamp,Matthias Schwarz Pdf

This volume contains a collection of well-written surveys provided by experts in Global Differential Geometry to give an overview over recent developments in Riemannian Geometry, Geometric Analysis and Symplectic Geometry. The papers are written for graduate students and researchers with a general interest in geometry, who want to get acquainted with the current trends in these central fields of modern mathematics.